Scientific Instrument Company

1. The precision Scientific Instrument Company manufactures thermometers that are supposed to give reading of 0 Celsius at the freezing point of water. The tests on a large sample of theses thermometers reveal that at the freezing point of water, some give reading below 0 Celsius. Assume that the mean reading in 0 Celsius and the standard deviation of the reading is 1.00 Celsius. Also assume that the frequency distribution of error closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information.
If 95 of the thermometer are rejected because they have reading that are too high, but all other thermometer are acceptable, find the temperature that separates the rejected thermometers from the others.

2. A bank's loan officer rates applicants for credit. The rating are normally distributed with a mean of 200 and standard deviation of 50. find P60, the score which separates the lower 605 from the top 40%.

3. The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?

4. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
Of 139 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.

5. Use the confidence level and sample data to find the margin of error. E.
College students' annual earnings; 99% confidence; n=74, sample mean=$3967, standard deviation= $874

6. Use the confidence level and sample data to find a confidence interval for estimating the population mean.
A group of 56 randomly selected students have a mean score of 30.8 with standard deviation of 4.5 on a placement test. What is the 90 percent confidence interval for the mean score, mean, of all students taking the test?